In this paper, the problem of stabilizing two scalar plants across a Gaussian multiple access channel (MAC) is addressed. Both states are encoded separately and sent across a shared MAC channel to a joint decoder/controller. A necessary condition for stabilizing such a system in the mean square sense is obtained using information-theoretic tools. This condition establishes the relationship between the magnitude of the unstable eigenvalues and the capacity region of Gaussian feedback multiple-access channel. A time-division encoding scheme along with a switched linear control law is proposed to achieve a rate region that is sufficient for stabilizability. The problem is studied both under the assumption that the two encoders can cooperate by sharing information and that they cannot. © 2013 AACC American Automatic Control Council.
CITATION STYLE
Liu, J., & Gupta, V. (2013). On stabilizability of LTI systems across a Gaussian MAC channel. In Proceedings of the American Control Conference (pp. 1556–1561). https://doi.org/10.1109/acc.2013.6580057
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